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Advances in Theoretical and Mathematical Physics: Theory and Applications
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Advances in Theoretical and Mathematical Physics: Theory and Applications

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Mathematical Physics".

Deadline for manuscript submissions: closed (31 October 2023) | Viewed by 7154

Special Issue Editor

Dr. Evgeny Mikhailov

E-Mail Website
Guest Editor
1. Faculty of Physics, Lomonosov Moscow State University, 119991 Moscow, Russia
2. Lebedev Physical Institute, 119991 Moscow, Russia
Interests: theoretical and mathematical physics; magnetohydrodynamics; dynamo theory; cosmic magnetism

Special Issue Information

Dear colleagues,

Mathematical methods in the natural sciences play an increasingly important role every year. The description of processes that have scales from elementary particles up to the Universe requires the construction of more and more complex mathematical models and the search for methods for solving corresponding equations. Mathematical methods also play an important role in applied problems requiring the solution of problems in continuum mechanics, electrodynamics, and others.

This special issue welcomes papers related to theoretical and mathematical physics. We would especially like to note the directions associated with field theory and related partial differential equations. It is interesting to construct their exact and approximate solutions, study the solvability of problems, and formulate theorems that describe the properties of solutions. We will also be glad to see works related to nonlinear effects in hydrodynamics and electrodynamics.

Although the special issue is mainly related to the theoretical study of mathematical models, we will also be glad to see papers where the equations are solved numerically. In general, we will be glad to see any work related to mathematical methods for solving actual problems in physics.

Dr. Evgeny Mikhailov
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Published Papers (6 papers)

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Research

21 pages, 1498 KiB  
Article
Projectile Motion in Special Theory of Relativity: Re-Investigation and New Dynamical Properties in Vacuum
by Ebrahem A. Algehyne, Abdelhalim Ebaid, Essam R. El-Zahar, Musaad S. Aldhabani, Mounirah Areshi and Hind K. Al-Jeaid
Mathematics 2023, 11(18), 3890; https://doi.org/10.3390/math11183890 - 13 Sep 2023
Viewed by 1039
Abstract
The projectile motion (PP) in a vacuum is re-examined in this paper, taking into account the relativistic mass in special relativity (SR). In the literature, the mass of the projectile was considered as a constant during motion. However, the mass of a projectile [...] Read more.
The projectile motion (PP) in a vacuum is re-examined in this paper, taking into account the relativistic mass in special relativity (SR). In the literature, the mass of the projectile was considered as a constant during motion. However, the mass of a projectile varies with velocity according to Einstein’s famous equation m=m01−v2/c2, where m0 is the rest mass of the projectile and c is the speed of light. The governing system consists of two-coupled nonlinear ordinary differential equations (NODEs) with prescribed initial conditions. An analytical approach is suggested to treat the current model. Explicit formulas are determined for the main characteristics of the relativistic projectile (RP) such as time of flight, time of maximum height, range, maximum height, and the trajectory. The relativistic results reduce to the corresponding ones of the non-relativistic projectile (NRP) in Newtonian mechanics, when the initial velocity is not comparable to c. It is revealed that the mass of the RP varies during the motion and an analytic formula for the instantaneous mass in terms of time is derived. Also, it is declared that the angle of maximum range of the RP depends on the launching velocity, i.e., unlike the NRP in which the angle of maximum range is always π/4. In addition, this angle lies in a certain interval [π/4,π/6) for any given initial velocity (<c). The obtained results are discussed and interpreted. Comparisons with a similar problem in the literature are performed and the differences in results are explained. Full article
(This article belongs to the Special Issue Advances in Theoretical and Mathematical Physics: Theory and Applications)
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17 pages, 3543 KiB  
Article
Calculation of the Magnetic Field of a Current-Carrying System
by Dmitrii Vinogradov, Igor Teplyakov and Yury Ivochkin
Mathematics 2023, 11(17), 3623; https://doi.org/10.3390/math11173623 - 22 Aug 2023
Viewed by 743
Abstract
With regard to the study of the characteristics of electrovortex flows occurring indirect current electric arcs and electroslag smelting furnaces, a method has been developed for calculating the magnetic field in a current-carrying medium based on the calculation of the Biot–Savart–Laplace integral. The [...] Read more.
With regard to the study of the characteristics of electrovortex flows occurring indirect current electric arcs and electroslag smelting furnaces, a method has been developed for calculating the magnetic field in a current-carrying medium based on the calculation of the Biot–Savart–Laplace integral. The developed technique is focused on the use of unstructured grids and does not require a priori information about the shape of the computational domain. The technique has been tested on problems that have an analytical solution, i.e., the calculation of the distribution of the magnetic field in the cylinder and the calculation of the magnetic field of the ring with the current. The distributions of the magnetic field are obtained for the two-dimensional and three-dimensional cases. We used NVIDIA CUDA technology on graphic processor units (GPUs) to speed up calculations. A comparison of the calculation times on various CPUs and GPUs is given. Full article
(This article belongs to the Special Issue Advances in Theoretical and Mathematical Physics: Theory and Applications)
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12 pages, 969 KiB  
Article
New Physical–Mathematical Analysis of Cardiac Dynamics and Temperature for the Diagnosis of Infectious Disease
by Leonardo Juan Ramirez Lopez, Sandra Catalina Correa Herrera and José Arturo Lagos Sandoval
Mathematics 2023, 11(15), 3374; https://doi.org/10.3390/math11153374 - 02 Aug 2023
Viewed by 808
Abstract
Background: Physical and mathematical theories have made it possible to generate methods for the characterization and diagnosis of physiological variables such as cardiac dynamics. Therefore, it would be useful to implement them to evaluate the dynamic changes in human physiology during the development [...] Read more.
Background: Physical and mathematical theories have made it possible to generate methods for the characterization and diagnosis of physiological variables such as cardiac dynamics. Therefore, it would be useful to implement them to evaluate the dynamic changes in human physiology during the development of COVID-19, which causes disease, severe respiratory and death. Objective: to establish a method for detecting possible alterations associated with COVID-19 through simulations of adult cardiac dynamics and body temperature using dynamic systems theory, probability, entropy and set theory. Methodology: simulations of cardiac dynamics were generated in subjects with 10 temperature ranges between 32 °C and 42 °C via numerical attractors after their evaluation using entropy proportions. Results: differences were observed in the proportions of entropy that differentiate normal cardiac dynamics and acute myocardial infarction towards progression to fever. Conclusion: the physical mathematical analysis of cardiac behavior in relation to body temperature in people with COVID-19 allowed the establishment of a possible surveillance method for detecting minor alterations. Full article
(This article belongs to the Special Issue Advances in Theoretical and Mathematical Physics: Theory and Applications)
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14 pages, 2150 KiB  
Article
Eigenvalue Problem for a Reduced Dynamo Model in Thick Astrophysical Discs
by Evgeny Mikhailov and Maria Pashentseva
Mathematics 2023, 11(14), 3106; https://doi.org/10.3390/math11143106 - 14 Jul 2023
Cited by 3 | Viewed by 683
Abstract
Magnetic fields of different astrophysical objects are generated by the dynamo mechanism. Dynamo is based on the alpha-effect and differential rotation, which are described using a system of parabolic equations. Their solution is an important problem in magnetohydrodynamics and mathematical physics. They can [...] Read more.
Magnetic fields of different astrophysical objects are generated by the dynamo mechanism. Dynamo is based on the alpha-effect and differential rotation, which are described using a system of parabolic equations. Their solution is an important problem in magnetohydrodynamics and mathematical physics. They can be solved assuming exponential growth of the solution, which leads to an eigenvalue problem for a differential operator connected with spatial coordinates. Here, we describe a system of equations connected with the generation of magnetic field in discs, which are associated with galaxies and binary systems. For an ideal case of an infinitely thin disc, the eigenvalue problem can be precisely solved. If we take into account the finite thickness of the disc, the problem becomes more difficult. The solution can be found using asymptotical methods based on perturbations of the eigenvalues. Here, we present two different models which describe field evolution for different cases. For the first, we find eigenvalues taking into account linear and quadratic terms for the perturbations in the eigenvalue problem. For the second, we find eigenvalues using only linear terms; this is quite sufficient. Results were verified through numerical modeling, and basic computational tests show proper correspondence between different methods. Full article
(This article belongs to the Special Issue Advances in Theoretical and Mathematical Physics: Theory and Applications)
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11 pages, 1784 KiB  
Article
Mathematical Physics of Time Dilation through Curved Trajectories with Applications
by Ayman Kamel, Abdelhalim Ebaid, Essam R. El-Zahar, Riadh Chteoui and Laila F. Seddek
Mathematics 2023, 11(10), 2402; https://doi.org/10.3390/math11102402 - 22 May 2023
Cited by 1 | Viewed by 2367
Abstract
In special relativity, the time dilation formula has been obtained by particles propagation in a straight line trajectory relative to an observer in motion. Up to now, there are no available formulas for other possible trajectories of particles. However, this paper obtains formulas [...] Read more.
In special relativity, the time dilation formula has been obtained by particles propagation in a straight line trajectory relative to an observer in motion. Up to now, there are no available formulas for other possible trajectories of particles. However, this paper obtains formulas of time dilation for several trajectories of particle such as parabolic, elliptic, and circular and finds a relatively accurate trajectory. The obtained formulas are employed in order to analyze the time dilation of the muon particles decay. In this paper, it is found that the time dilation of the parabolic and the elliptical trajectories exceed the corresponding results utilizing the standard Lorentz-Einstein time dilation formula. Consequently, if we are able to control the trajectory of unstable particles by some external forces, then their life-times might be increased. Probably, the increase in lifetime via a curved trajectory occurs at lower relative velocity & acceleration energy if compared to the straight line trajectory. In addition, the circular trajectory leads to multiple values of time dilation at certain velocities of an observer in motion, which may give an interpretation of fluctuations of time dilation in quantum mechanics. The result arises from the present relatively accurate formula of time dilation that is very close to the experimental data of muon decay (CERN experiment) when it is compared to the result obtained by the Lorentz-Einstein formula. Finally, it may be concluded that the time dilation not only depends on relative velocity and acceleration energy of particles but also on curved trajectories. The present work may attract other researchers to study different trajectories. Full article
(This article belongs to the Special Issue Advances in Theoretical and Mathematical Physics: Theory and Applications)
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11 pages, 5750 KiB  
Article
Surface Family Pair with Bertrand Pair as Common Geodesic Curves in Galilean 3-Space 𝔾3
by Areej A. Almoneef and Rashad A. Abdel-Baky
Mathematics 2023, 11(10), 2391; https://doi.org/10.3390/math11102391 - 22 May 2023
Cited by 2 | Viewed by 841
Abstract
This paper is about deriving the necessary and sufficient conditions of a surface family pair with a Bertrand pair as common geodesic curves in Galilean 3-space G3. Thereafter, the consequence for the ruled surface family pair is also deduced. Meanwhile, some [...] Read more.
This paper is about deriving the necessary and sufficient conditions of a surface family pair with a Bertrand pair as common geodesic curves in Galilean 3-space G3. Thereafter, the consequence for the ruled surface family pair is also deduced. Meanwhile, some examples are provided to show the surfaces family with common Bertrand geodesic curves. Full article
(This article belongs to the Special Issue Advances in Theoretical and Mathematical Physics: Theory and Applications)
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